The third-seeded Coria lost only six games in routing the fourth-seeded Schuettler, 6-2, 6-1, 6-3, for his second Masters Series title.
Coria, who also won in Hamburg last year, claimed his 26th straight match win on clay and spoiled Schuettler's 28th birthday. It was his 12th overall ATP Tour title.
The 22-year-old become the first Argentine to win in Monte Carlo since his former coach, Alberto Mancini, in 1989.
Coria appeared in his second straight ATP Masters Series finale. He reached the final last week against Andy Roddick at the NASDAQ-100 Open in Miami, but was forced to retire in the fourth set with a back injury.
Coria's winning streak on clay is the longest since Thomas Muster won 40 in 1995.
Celebrity Couples of 2014 [PHOTOS]